RD Sharma XI 2019 Solutions for Class 11 Science Math Chapter 2 Relations are provided here with simple step-by-step explanations. These solutions for Relations are extremely popular among class 11 Science students for Math Relations Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RD Sharma XI 2019 Book of class 11 Science Math Chapter 2 are provided here for you for free. You will also love the ad-free experience on Meritnation’s RD Sharma XI 2019 Solutions. All RD Sharma XI 2019 Solutions for class 11 Science Math are prepared by experts and are 100% accurate.

Answer:

(i) {(1, 6), (3, 4), (5, 2)}
Since it is not a subset of A × B, it is not a relation from A to B.
(ii) {(1, 5), (2, 6), (3, 4), (3, 6)}
Since it is a subset of A × B, it is a relation from A to B.
(iii) {(4, 2), (4, 3), (5, 1)}
Since it is not a subset of A × B, it is not a relation from A to B.
(iv) A × B
Since it is a subset (equal to) of A × B, it is a relation from A to B.

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Question 2:

A relation R is defined from a set A = [2, 3, 4, 5] to a set B = [3, 6, 7, 10] as follows:
(x, y) ∈ R ⇔ x is relatively prime to y
Express R as a set of ordered pairs and determine its domain and range.

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Question 3:

Let A be the set of first five natural numbers and let R be a relation on A defined as follows:
(x, y) ∈ R ⇔ x ≤ y
Express R and R−1 as sets of ordered pairs. Determine also (i) the domain of R−1 (ii) the range of R.

Page No 2.21:

Question 7:

Let A = (3, 5) and B = (7, 11). Let R = {(a, b) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.

Answer:

Given:
A = (3, 5) and B = (7, 11)
Also,
R = {(a, b) : a ∈ A, b ∈ B, a − b is odd}a are the elements of A and b are the elements of B.

∴a-b=3-7,3-11,5-7,5-11⇒a-b=-4,-8,-2,-6Here,a-bisalwaysanevennumber.
So, R is an empty relation from A to B.
Hence proved.

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Question 8:

Let A = [1, 2] and B = [3, 4]. Find the total number of relation from A into B.

Answer:

We have:
A = {1, 2} and B = {3, 4}
Now,n(A×B)=n(A)×n(B)=2×2=4
There are 2n relations from A to B, where n is the number of elements in their Cartesian product.
∴ Number of relations from A to B is 24 = 16.

Page No 2.21:

Question 15:

Define a relation R on the set N of natural number by R = {(x, y) : y = x + 5, x is a natural number less than 4, x, y ∈ N}. Depict this relationship using (i) roster form (ii) an arrow diagram. Write down the domain and range or R.

Answer:

Page No 2.8:

Question 4:

If a ∈ [2, 4, 6, 9] and b ∈ [4, 6, 18, 27], then form the set of all ordered pairs (a, b) such that a divides b and a < b.

Answer:

Given:a ∈ [2, 4, 6, 9] and b ∈ [4, 6, 18, 27]
Here,
2 divides 4, 6 and 18 and 2 is less than all of them.
6 divides 18 and 6 and 6 is less than 18.
9 divides 18 and 27 and 9 is less than 18 and 27.
Now,
Set of all ordered pairs (a, b) such that a divides b and a < b = {(2, 4), (2, 6), (2, 18), (6, 18), (9, 18), (9, 27)}

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Question 5:

Answer:

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Question 6:

Let A = {1, 2, 3} and B = {3, 4}. Find A × B and show it graphically.

Answer:

Given:A = {1, 2, 3} and B = {3, 4}
Now,A × B = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}
To represent A × B graphically, follow the given steps:
(a) Draw two mutually perpendicular lines—one horizontal and one vertical.
(b) On the horizontal line, represent the elements of set A; and on the vertical line, represent the elements of set B.
(c) Draw vertical dotted lines through points representing elements of set A on the horizontal line and horizontal lines through points representing elements of set B on the vertical line.
The points of intersection of these lines will represent A × B graphically.